Finite Group Databasebeta

← #6611335

Subgroups — #6611335

Order 512.

1894 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36189C211yesmaximal, characteristic, complemented
2#36127C211yesmaximal, characteristic
3#33232C211yesmaximal, characteristic, complemented
4#33049C211yesmaximal, characteristic, complemented
5#33043C211yesmaximal, characteristic, complemented
6#29143C211yesmaximal, characteristic, complemented
7#28748C211yesmaximal, characteristic, complemented
8#27975C211yesmaximal, characteristic, complemented
9#27972C211yesmaximal, characteristic, complemented
10#27764C214yesmaximal, complemented
11#27284C214yesmaximal, complemented
12#27267C214yesmaximal, complemented
13#25857C211yesmaximal, characteristic, complemented
14#25857C211yesmaximal, characteristic, complemented
15#22420C214yesmaximal, complemented
16#21646C211yesmaximal, characteristic, complemented
17#21200C211yesmaximal, characteristic, complemented
18#21195C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic, complemented
20C2×#547C2212yes—
21C2×#532C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C2×#491C2214yes—
24C2×#487C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#435C2212yes—
28C2×#417C2214yes—
29C2×#416C2214yes—
30C2×C4×M16C2211yescharacteristic
31C22×C4×C8C2211yescharacteristic
32#2868C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2570C2212yes—
39#2547C2212yes—
40#2537—21no—
41#2537—21no—
42#2511—21no—
43#2507—21no—
44#2497—21no—
45#2487—21no—
46#2442C2212yes—
47#2441C2212yes—
48#2432C2212yes—
49#2432C2212yes—
50#2423—21no—
51#2422—21no—
52#2422—21no—
53#2422—21no—
54#2422—21no—
55#2417—21no—
56#2360—21no—
57#2352C2212yes—
58D4×C4⋊C4—21no—
59D4×C4⋊C4—21no—
60#2345—21no—
61C4×C4⋊Q8C2211yescharacteristic
62C4×#127C2211yescharacteristic
63#2285C2211yescharacteristic
64C2×#384C2211yescharacteristic
65C42×D4C2211yescharacteristic
66#2074C2214yes—
67#2072C2214yes—
68#2043C2214yes—
69#2042C2214yes—
70#2042C2214yes—
71#2025C2214yes—
72#1990C2211yescharacteristic
73#1981C2214yes—
74#1960C2214yes—
75#1959C2214yes—
76#1958C2214yes—
77#1957C2211yescharacteristic
78#1957C2211yescharacteristic
79#1957C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1936C2214yes—
87#1935C2214yes—
88#1933C2214yes—
89#1894C2214yes—
90#1892C2214yes—
91#1873C2214yes—
92#1872C2214yes—
93#1834C2211yescharacteristic
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1804C2214yes—
97#1788C2214yes—
98#1788C2214yes—
99#1771C2212yes—
100C4×C4⋊C8C2211yescharacteristic
101#1762C2214yes—
102#1753C2212yes—
103#1752C2212yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C22×#41C2312yes—
108C22×#41C2312yes—
109C22×M16C2312yes—
110C23×C8C2312yes—
111#547—216no—
112#532—24no—
113#532—24no—
114#532—42no—
115#532—42no—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2312yes—
119C2×C4⋊Q8C2312yes—
120C2×C4⋊Q8C2311yescharacteristic
121C2×#127C2311yescharacteristic
122C2×#125C2312yes—
123C2×#124C2312yes—
124C2×#124C2312yes—
125C2×#123—22no—
126C2×#123—22no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2312yes—
131C2×#121—22no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×C4×Q8—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4—21no—
143C2×C4×D4D411yescharacteristic
144C2×C4×D4D411yescharacteristic
145C2×C4×D4C2312yes—
146C2×C4×D4C2311yescharacteristic
147C2×#117C2312yes—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—22no—
151C22×C4⋊C4C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#491—48no—
155#487—42no—
156#487—42no—
157#486—24no—
158#435—28no—
159C2×C4⋊C8C2312yes—
160#417—48no—
161#416—48no—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C4×M16—42no—
177C2×#97C2312yes—
178C2×#97C2312yes—
179C2×#97C2312yes—
180C2×C4×C8—42no—
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2311yescharacteristic
184C2×C4×C8C2311yescharacteristic
185C2×C4×C8C2312yes—
186#400—22no—
187#400—22no—
188#399—22no—
189#398—22no—
190#398—22no—
191#397—22no—
192#397—22no—
193#396—22no—
194#394—22no—
195#394—22no—
196#394—22no—
197#394—22no—
198#391—21no—
199#391—21no—
200#391—21no—
201#391C2312yes—
202#391C2312yes—
203#390—21no—
204#390—21no—
205#390C2312yes—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—22no—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#388—22no—
222#387—22no—
223#387—22no—
224#387—22no—
225#387—22no—
226#386—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#384—21no—
233#384—21no—
234#384—21no—
235#384—21no—
236#384—21no—
237#384—21no—
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#384C2312yes—
241#384C2311yescharacteristic
242#384C2311yescharacteristic
243#382C2312yes—
244#382C2312yes—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—22no—
254#380—22no—
255#380—22no—
256#380C2312yes—
257#380C2312yes—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—21no—
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4D411yescharacteristic
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2311yescharacteristic
265C4×C22⋊C4—22no—
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4D411yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271C4×C22⋊C4C2311yescharacteristic
272C43C2311yescharacteristic
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C2×#41—24no—
281C2×#41—24no—
282C2×#41—28no—
283C2×#41—28no—
284C2×#41—42no—
285C2×#41—42no—
286C2×#41—44no—
287C2×#41—44no—
288C22×Q8—21no—
289C22×Q8C2412yes—
290C22×Q8C2412yes—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4C2×D411yescharacteristic
296C22×D4C2412yes—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C2×M16—24no—
308C2×M16—24no—
309C2×M16—42no—
310C22×C8—24no—
311C22×C8—24no—
312C22×C8—42no—
313C22×C8C2412yes—
314C22×C8C2412yes—
315C22×C8C2412yes—
316C22×C8C2412yes—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319C4⋊Q8—22no—
320C4⋊Q8—28no—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—44no—
325#127—22no—
326#127#4114yes—
327#125—44no—
328#124—24no—
329#124—24no—
330#124—42no—
331#124—42no—
332#123—48no—
333#123—48no—
334C22⋊Q8—28no—
335C22⋊Q8—28no—
336C22⋊Q8—44no—
337C22⋊Q8—82no—
338#121—44no—
339#121—44no—
340#121—44no—
341#121—44no—
342#121—48no—
343C4×Q8—82no—
344C4×D4—28no—
345C4×D4—42no—
346C4×D4—42no—
347C4×D4—44no—
348C4×D4—44no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4#4118yes—
354#117—44no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—48no—
385C2×C4⋊C4—82no—
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2×D411yescharacteristic
388C2×C4⋊C4C2×D411yescharacteristic
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C22⋊C4C2×D411yescharacteristic
410C2×C22⋊C4C2×D411yescharacteristic
411C2×C22⋊C4C2×D411yescharacteristic
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C4⋊C8—24no—
432#103—28no—
433#103—28no—
434#103—44no—
435#103—44no—
436#103—44no—
437#103—44no—
438#103—44no—
439#103—44no—
440#102—28no—
441#102—28no—
442#102—44no—
443#102—44no—
444C22⋊C8—24no—
445C22⋊C8—24no—
446#97—24no—
447#97—24no—
448#97—42no—
449C4×C8—22no—
450C4×C8—22no—
451C4×C8—22no—
452C4×C8—22no—
453C4×C8—42no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472#95C2×D411yescharacteristic
473#95C2×D411yescharacteristic
474C24—22no—
475C24C22×D411yescharacteristic
476C24C22×D411yescharacteristic
477#41—416no—
478#41—416no—
479#41—88no—
480#41—88no—
481C2×Q8—24no—
482C2×Q8—24no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—24no—
486C2×Q8—24no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—41no—
498C2×D4—41no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—82no—
508C2×D4—82no—
509C2×D4#12414yes—
510C2×D4C2×#4114yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4—82no—
547C22×C4—82no—
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C2×#4114yes—
561C22×C4C2×#4114yes—
562C22×C4C2511yescharacteristic
563M16—48no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—48no—
576C2×C8H(5,𝔽2)14yes—
577C4⋊C4—22no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—44no—
590C4⋊C4—44no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—82no—
605C4⋊C4—82no—
606C4⋊C4—82no—
607C4⋊C4—82no—
608C4⋊C4—82no—
609C4⋊C4—82no—
610C4⋊C4—82no—
611C4⋊C4—82no—
612C4⋊C4#12414yes—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—82no—
628C22⋊C4—82no—
629C22⋊C4#12414yes—
630C22⋊C4#12414yes—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—22no—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—22no—
643C42—21no—
644C42—82no—
645C42—82no—
646C42C2×#4114yes—
647C42C2×#4112yes—
648C42H(5,𝔽2)12yes—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—24no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23C2×#12412yes—
669C23C2×#12412yes—
670C23C23×D411yescharacteristic
671Q8—44no—
672Q8—44no—
673Q8—44no—
674Q8—44no—
675Q8—84no—
676D4—28no—
677D4—44no—
678D4—44no—
679D4—48no—
680D4—48no—
681D4—88no—
682D4—88no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—88no—
739C2×C4—88no—
740C2×C4—88no—
741C2×C4—164no—
742C2×C4C2×#12412yes—
743C2×C4C2×#12412yes—
744C2×C4C2×#12412yes—
745C2×C4C2×#12412yes—
746C2×C4#54612yes—
747C2×C4#54612yes—
748C2×C4#57512yes—
749C2×C4#57512yes—
750C2×C4#57712yes—
751C2×C4#57812yes—
752C2×C4C22×#4111yescharacteristic
753C2×C4C22×#4112yes—
754C2×C4C2×H(5,𝔽2)12yes—
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C8—24no—
757C8—42no—
758C8—42no—
759C8—42no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22C22×#12411yescharacteristic
782C22C2×#54611yescharacteristic
783C22#349811yescharacteristic
784C22C2×#57511yescharacteristic
785C22C2×#57511yescharacteristic
786C22C2×#57711yescharacteristic
787C22C2×#57811yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4#330714yes—
806C4#331514yes—
807C4#348112yes—
808C4#351912yes—
809C2—42no—
810C2—42no—
811C2—84no—
812C2#3628911yescharacteristic
813C2#6061811yescharacteristic
814C2#6062311yescharacteristic
815C2C2×#330711yescharacteristic
816C2C2×#331511yescharacteristic
817C2#6242511yescharacteristic
818C2#6242711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #36189C2semidirect
3. #33232C2semidirect
4. #33049C2semidirect
5. #33043C2semidirect
6. #29143C2semidirect
7. #28748C2semidirect
8. #27975C2semidirect
9. #27972C2semidirect
10. #27764C2semidirect
11. #27284C2semidirect
12. #27267C2semidirect
13. #25857C2semidirect
14. #25857C2semidirect
15. #22420C2semidirect
16. #21646C2semidirect
17. #21200C2semidirect
18. #21195C2semidirect
19. C4×#435C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#361892
#361272
#332322
#330492
#330432
#291432
#287482
#279752
#279722
#277642
#272842
#272672
#258572
#224202
#216462
#212002
#211952
C4×#4352